In the classic linear assignment problem, items must be assigned to agents in a manner that minimizes the sum of the costs for each item-agent assignment, where the costs of all possible item-agent pairings are observed in advance. This is a well-known and well-characterized problem, and algorithms exist to attain the solution. In contrast, less attention has been given to the dynamic version of this problem where each item must be assigned to an agent sequentially upon arrival without knowledge of the future items to arrive. Motivated by an application in the globally pressing domain of international asylum and refugee resettlement, specifically that of matching refugees and asylum seekers to geographic localities within a host country, this study proposes an assignment mechanism that combines linear assignment programming solutions with stochastic programming methods to minimize the expected loss when assignments must be made in this dynamic sequential fashion, and offers an algorithm for implementing the mechanism. The study also presents an approximate version of the mechanism and accompanying algorithm that is more computationally efficient, a prediction-based alternative approximation that combines stochastic programming with machine learning to achieve even greater efficiency, as well as heuristic mechanisms. In addition, the study provides an extension to dynamic batch assignment, where items arrive and must be assigned sequentially in groups. Real-world refugee resettlement data in the United States are used to illustrate the methods and show how they could be practically implemented in order to optimize refugees' and asylum seekers' employment prospects (or other integration outcomes) in their host countries.

中文翻译：

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一种最低风险的动态分配机制以及对难民匹配的近似、扩展和应用

在经典的线性分配问题中，必须以最小化每个项目-代理分配的成本总和的方式将项目分配给代理，其中预先观察所有可能的项目-代理配对的成本。这是一个众所周知且特征明确的问题，并且存在获得解决方案的算法。相比之下，这个问题的动态版本很少受到关注，其中每个项目必须在到达时按顺序分配给代理，而无需知道未来要到达的项目。受到国际庇护和难民重新安置这一全球紧迫领域的申请的启发，特别是将难民和寻求庇护者与东道国的地理区域相匹配的申请，本研究提出了一种分配机制，该机制将线性分配规划解决方案与随机规划方法相结合，以在必须以这种动态顺序方式进行分配时最小化预期损失，并提供实现该机制的算法。该研究还提出了该机制的近似版本和计算效率更高的伴随算法，一种基于预测的替代近似，将随机编程与机器学习相结合以实现更高的效率，以及启发式机制。此外，该研究为动态批次分配提供了扩展，其中项目到达并且必须按组顺序分配。